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All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Progress on Variable Cycle Engines

Progress in the development and future requirements of the Variable Stream Control Engine (VSCE) are presented. The two most critical components of this advanced system for future supersonic transports, the high performance duct burner for thrust augmentation, and the low jet coannular nozzle were studied. Nozzle model tests substantiated the jet noise benefit associated with the unique velocity profile possible with a coannular nozzle system on a VSCE. Additional nozzle model performance tests have established high thrust efficiency levels only at takeoff and supersonic cruise for this nozzle system. An experimental program involving both isolated component and complete engine tests has been conducted for the high performance, low emissions duct burner with good results and large scale testing of these two components is being conducted using a F100 engine as the testbed for simulating the VSCE. Future work includes application of computer programs for supersonic flow fields to coannular nozzle geometries, further experimental testing with the duct burner segment rig, and the use of the Variable Cycle Engine (VCE) Testbed Program for evaluating the VSCE duct burner and coannular nozzle technologies.

Westmoreland, J. S.↗
NASA NTRS1995

Mississippi State University Center for Air Sea Technology FY95 Research Program

The Mississippi State University (MSU) Center for Air Sea Technology (CAST) evolved from the Institute for Naval Oceanography's (INO) Experimental Center for Mesoscale Ocean Prediction (ECMOP) which was started in 1989. MSU CAST subsequently began operation on 1 October 1992 under an Office of Naval Research (ONR) two-year grant which ended on 30 September 1994. In FY95 MSU CAST was successful in obtaining five additional research grants from ONR, as well as several other research contracts from the Naval Oceanographic Office via NASA, the Naval Research Laboratory, the Army Corps of Engineers, and private industry. In the past, MSU CAST technical research and development has produced tools, systems, techniques, and procedures that improve efficiency and overcome deficiency for both the operational and research communities residing with the Department of Defense, private industry, and university ocean modeling community. We continued this effort with the following thrust areas: to develop advanced methodologies and tools for model evaluation, validation and visualization, both oceanographic and atmospheric; to develop a system-level capability for conducting temporally and ; spatially scaled ocean simulations driven by or are responsive to ocean models, and take into consideration coupling to atmospheric models; to continue the existing oceanographic/atmospheric data management task with emphasis on distributed databases in a network environment, with database optimization and standardization, including use of Mosaic and World Wide Web (WWW) access; and to implement a high performance parallel computing technology for CAST ocean models

Yeske, Lanny↗
NASA NTRS1993

Control structural interaction testbed: A model for multiple flexible body verification

Conventional end-to-end ground tests for verification of control system performance become increasingly complicated with the development of large, multiple flexible body spacecraft structures. The expense of accurately reproducing the on-orbit dynamic environment and the attendant difficulties in reducing and accounting for ground test effects limits the value of these tests. TRW has developed a building block approach whereby a combination of analysis, simulation, and test has replaced end-to-end performance verification by ground test. Tests are performed at the component, subsystem, and system level on engineering testbeds. These tests are aimed at authenticating models to be used in end-to-end performance verification simulations: component and subassembly engineering tests and analyses establish models and critical parameters, unit level engineering and acceptance tests refine models, and subsystem level tests confirm the models' overall behavior. The Precision Control of Agile Spacecraft (PCAS) project has developed a control structural interaction testbed with a multibody flexible structure to investigate new methods of precision control. This testbed is a model for TRW's approach to verifying control system performance. This approach has several advantages: (1) no allocation for test measurement errors is required, increasing flight hardware design allocations; (2) the approach permits greater latitude in investigating off-nominal conditions and parametric sensitivities; and (3) the simulation approach is cost effective, because the investment is in understanding the root behavior of the flight hardware and not in the ground test equipment and environment.

Chory, M. A.↗
NASA NTRS2009

Lunar Surface Stirling Power Systems Using Am-241

For many years NASA has used the decay of Pu-238 (in the form of the General Purpose Heat Source (GPHS)) as a heat source for Radioisotope Thermoelectric Generators (RTG), which have provided electrical power for many NASA missions. While RTG's have an impressive reliability record for the missions in which they have been used, their relatively low thermal to electric conversion efficiency (-5% efficiency) and the scarcity of Plutoinium-238 (Pu-238) has led NASA to consider other power conversion technologies. NASA is considering returning both robotic and human missions to the lunar surface and, because of the long lunar nights (14 earth days) isotope power systems are an attractive candidate to generate electrical power. NASA is currently developing the Advanced Stirling Radioisotope Generator (ASRG) as a candidate higher efficiency power system that produces greater than 160 watts with 2 GPHS modules at the beginning of life (BOL) (-30% efficiency). The ASRG uses the same Pu-238 GPHS modules, which are used in RTG, but by coupling them to a Stirling convertor provides a 4-fold reduction in the number of GPHS modules. This study considers the use of Americium 241 (Am-241) as a substitute for the Pu-238 in Stirling convertor based Radioisotope Power Systems (RPS) for power levels from 1 O's of watts to 5 kWe. The Am-241 is used as a replacement for the Pu-238 in GPHS modules. Depending on power level, different Stirling heat input and removal systems are modeled. It was found that substituting Am-241 GPHS modules into the ASRG reduces power output by about 1/5 while maintaining approximately the same system mass. In order to obtain the nominal 160 watts electrical output of the Pu-238 ASRG requires 10 Am-241 GPHS modules. Higher power systems require changing from conductive coupling heat input and removal from the Stirling convertor to either pumped loops or heat pipes. Liquid metal pumped loops are considered as the primary heat transportation on the hot end and water pumped loop/heat pipe radiator is considered for the heat rejection side for power levels above 1 kWe.

Schmitz, Paul C.↗
NASA NTRS2010

Lunar Surface Stirling Power Systems Using Isotope Heat Sources

For many years, NASA has used the decay of plutonium-238 (Pu-238) (in the form of the General Purpose Heat Source (GPHS)) as a heat source for Radioisotope Thermoelectric Generators (RTGs), which have provided electrical power for many NASA missions. While RTGs have an impressive reliability record for the missions in which they have been used, their relatively low thermal to electric conversion efficiency and the scarcity of plutonium-238 (Pu-238) has led NASA to consider other power conversion technologies. NASA is considering returning both robotic and human missions to the lunar surface and, because of the long lunar nights (14.75 Earth days), isotope power systems are an attractive candidate to generate electrical power. NASA is currently developing the Advanced Stirling Radioisotope Generator (ASRG) as a candidate higher efficiency power system that produces greater than 160 W with two GPHS modules at the beginning of life (BOL) (~32% efficiency). The ASRG uses the same Pu-238 GPHS modules, which are used in RTG, but by coupling them to a Stirling convertor provides a four-fold reduction in the number of GPHS modules. This study considers the use of americium-241 (Am-241) as a substitute for the Pu-238 in Stirling- convertor-based Radioisotope Power Systems (RPS) for power levels from tens of watts to 5 kWe. The Am-241 is used as a substitute for the Pu-238 in GPHS modules. Depending on power level, different Stirling heat input and removal systems are modeled. It was found that substituting Am-241 GPHS modules into the ASRG reduces power output by about one-fifth while maintaining approximately the same system mass. In order to obtain the nominal 160 W of electrical output of the Pu-238 ASRG requires 10 Am-241 GPHS modules. Higher power systems require changing from conductive coupling heat input and removal from the Stirling convertor to either pumped loops or heat pipes. Liquid metal pumped loops are considered as the primary heat transportation on the hot end and water pumped loop/heat pipe radiator is considered for the heat rejection side for power levels above 1 kWe.

Schmitz, Paul C.↗
NASA NTRS2019

Technology Development and Infusion by NASA's Entry Systems Modeling Project

This presentation describes recent development of modeling and simulation technologies by NASA's Entry Systems Modeling Project and their infusion into the Agency's exploration missions. Technology development is organized and prioritized using a system-level perspective, resulting in four broad technical areas of investment: (1) Thermal protection material modeling, (2) Shock layer kinetics and radiation, (3) Computational and experimental aerosciences, and (4) Guidance, navigation, and control. The presentation will illustrate how applied research can meaningfully impact flight programs by highlighting a few recent contributions: Orion and Mars 2020 radiative heating margin policy; Study of radiative heating at Titan; Aerothermal-mechanical erosion due to dust at Mars; Modeling the PICA-NuSil system; and contributions to modeling of parachutes for entry systems.

Barnhardt, Michael D.↗
NASA NTRS2003

Connecting Atmospheric Science and Atmospheric Models for Aerocaptured Missions to Titan and the Outer Planets

Many atmospheric measurement systems, such as the sounding instruments on Voyager, gather atmospheric information in the form of temperature versus pressure level. In these terms, there is considerable consistency among the mean atmospheric profiles of the outer planets Jupiter through Neptune, including Titan. On a given planet or on Titan, the range of variability of temperature versus pressure level due to seasonal, latitudinal, and diurnal variations is also not large. However, many engineering needs for atmospheric models relate not to temperature versus pressure level but atmospheric density versus geometric altitude. This need is especially true for design and analysis of aerocapture systems. Aerocapture drag force available for aerocapture is directly proportional to atmospheric density. Available aerocapture "corridor width" (allowable range of atmospheric entry angle) also depends on height rate of change of atmospheric density, as characterized by density scale height. Characteristics of hydrostatics and the gas law equation mean that relatively small systematic differences in temperature-versus-pressure profiles can integrate at high altitudes to very large differences in density-versus-altitude profiles. Thus a given periapsis density required to accomplish successful aerocapture can occur at substantially different altitudes (approx. 150 - 300 km) on the various outer planets, and significantly different density scale heights (approx. 20 - 50 km) can occur at these periapsis altitudes. This paper will illustrate these effects and discuss implications for improvements in atmospheric measurements to yield significant impact on design of aerocapture systems for future missions to Titan and the outer planets. Relatively small- scale atmospheric perturbations, such as gravity waves, tides, and other atmospheric variations can also have significant effect on design details for aerocapture guidance and control systems. This paper will also discuss benefits that would result from improved understanding of Titan and outer planetary atmospheric perturbation characteristics. Details of recent engineering-level atmospheric models for Titan and Neptune will be presented, and effects of present and future levels of atmospheric uncertainty and variability characteristics will be examined.

Justus, C. G.↗
NASA NTRS1986

Computational approaches to vision

Vision is examined in terms of a computational process, and the competence, structure, and control of computer vision systems are analyzed. Theoretical and experimental data on the formation of a computer vision system are discussed. Consideration is given to early vision, the recovery of intrinsic surface characteristics, higher levels of interpretation, and system integration and control. A computational visual processing model is proposed and its architecture and operation are described. Examples of state-of-the-art vision systems, which include some of the levels of representation and processing mechanisms, are presented.

Barrow, H. G.↗
NASA NTRS2013

Integrating Wind Profiling Radars and Radiosonde Observations with Model Point Data to Develop a Decision Support Tool to Assess Upper-Level Winds for Space Launch

On the day-of-launch, the 45th Weather Squadron (45 WS) Launch Weather Officers (LWOs) monitor the upper-level winds for their launch customers to include NASA's Launch Services Program and NASA's Ground Systems Development and Operations Program. They currently do not have the capability to display and overlay profiles of upper-level observations and numerical weather prediction model forecasts. The LWOs requested the Applied Meteorology Unit (AMU) develop a tool in the form of a graphical user interface (GUI) that will allow them to plot upper-level wind speed and direction observations from the Kennedy Space Center (KSC) 50 MHz tropospheric wind profiling radar, KSC Shuttle Landing Facility 915 MHz boundary layer wind profiling radar and Cape Canaveral Air Force Station (CCAFS) Automated Meteorological Processing System (AMPS) radiosondes, and then overlay forecast wind profiles from the model point data including the North American Mesoscale (NAM) model, Rapid Refresh (RAP) model and Global Forecast System (GFS) model to assess the performance of these models. The AMU developed an Excel-based tool that provides an objective method for the LWOs to compare the model-forecast upper-level winds to the KSC wind profiling radars and CCAFS AMPS observations to assess the model potential to accurately forecast changes in the upperlevel profile through the launch count. The AMU wrote Excel Visual Basic for Applications (VBA) scripts to automatically retrieve model point data for CCAFS (XMR) from the Iowa State University Archive Data Server (http://mtarchive.qeol.iastate.edu) and the 50 MHz, 915 MHz and AMPS observations from the NASA/KSC Spaceport Weather Data Archive web site (http://trmm.ksc.nasa.gov). The AMU then developed code in Excel VBA to automatically ingest and format the observations and model point data in Excel to ready the data for generating Excel charts for the LWO's. The resulting charts allow the LWOs to independently initialize the three models 0-hour forecasts against the observations to determine which is the best performing model and then overlay the model forecasts on time-matched observations during the launch countdown to further assess the model performance and forecasts. This paper will demonstrate integration of observed and predicted atmospheric conditions into a decision support tool and demonstrate how the GUI is implemented in operations.

Bauman, William H., III↗
NASA NTRS2009

Complexity for Survival of Living Systems

A logical connection between the survivability of living systems and the complexity of their behavior (equivalently, mental complexity) has been established. This connection is an important intermediate result of continuing research on mathematical models that could constitute a unified representation of the evolution of both living and non-living systems. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the two most relevant being Characteristics of Dynamics of Intelligent Systems (NPO- 21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; and Self-Supervised Dynamical Systems (NPO- 30634) NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72. As used here, living systems is synonymous with active systems and intelligent systems. The quoted terms can signify artificial agents (e.g., suitably programmed computers) or natural biological systems ranging from single-cell organisms at one extreme to the whole of human society at the other extreme. One of the requirements that must be satisfied in mathematical modeling of living systems is reconciliation of evolution of life with the second law of thermodynamics. In the approach followed in this research, this reconciliation is effected by means of a model, inspired partly by quantum mechanics, in which the quantum potential is replaced with an information potential. The model captures the most fundamental property of life - the ability to evolve from disorder to order without any external interference. The model incorporates the equations of classical dynamics, including Newton s equations of motion and equations for random components caused by uncertainties in initial conditions and by Langevin forces. The equations of classical dynamics are coupled with corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces that are gradients of the information potential, which, in turn, is a function of the probability densities. The probability densities are associated with mental images both self-image and nonself images (images of external objects that can include other agents). The evolution of the probability densities represents mental dynamics. Then the interaction between the physical and metal aspects of behavior is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. The interaction of a system with its self and nonself images affords unlimited capacity for increase of complexity. There is a biological basis for this model of mental dynamics in the discovery of mirror neurons that learn by imitation. The levels of complexity attained by use of this model match those observed in living systems. To establish a mechanism for increasing the complexity of dynamics of an active system, the model enables exploitation of a chain of reflections exemplified by questions of the form, "What do you think that I think that you think...?" Mathematically, each level of reflection is represented in the form of an attractor performing the corresponding level of abstraction with more details removed from higher levels. The model can be used to describe the behaviors, not only of biological systems, but also of ecological, social, and economics ones.

Zak, Michail↗
NASA NTRS2005

Construction of Covariance Functions with Variable Length Fields

This article focuses on construction, directly in physical space, of three-dimensional covariance functions parametrized by a tunable length field, and on an application of this theory to reproduce the Quasi-Biennial Oscillation (QBO) in the Goddard Earth Observing System, Version 4 (GEOS-4) data assimilation system. These Covariance models are referred to as multi-level or nonseparable, to associate them with the application where a multi-level covariance with a large troposphere to stratosphere length field gradient is used to reproduce the QBO from sparse radiosonde observations in the tropical lower stratosphere. The multi-level covariance functions extend well-known single level covariance functions depending only on a length scale. Generalizations of the first- and third-order autoregressive covariances in three dimensions are given, providing multi-level covariances with zero and three derivatives at zero separation, respectively. Multi-level piecewise rational covariances with two continuous derivatives at zero separation are also provided. Multi-level powerlaw covariances are constructed with continuous derivatives of all orders. Additional multi-level covariance functions are constructed using the Schur product of single and multi-level covariance functions. A multi-level powerlaw covariance used to reproduce the QBO in GEOS-4 is described along with details of the assimilation experiments. The new covariance model is shown to represent the vertical wind shear associated with the QBO much more effectively than in the baseline GEOS-4 system.

Gaspari, Gregory↗
NASA NTRS2012

The Development of Models for Carbon Dioxide Reduction Technologies for Spacecraft Air Revitalization

Through the respiration process, humans consume oxygen (O2) while producing carbon dioxide (CO2) and water (H2O) as byproducts. For long term space exploration, CO2 concentration in the atmosphere must be managed to prevent hypercapnia. Moreover, CO2 can be used as a source of oxygen through chemical reduction serving to minimize the amount of oxygen required at launch. Reduction can be achieved through a number of techniques. NASA is currently exploring the Sabatier reaction, the Bosch reaction, and co- electrolysis of CO2 and H2O for this process. Proof-of-concept experiments and prototype units for all three processes have proven capable of returning useful commodities for space exploration. All three techniques have demonstrated the capacity to reduce CO2 in the laboratory, yet there is interest in understanding how all three techniques would perform at a system level within a spacecraft. Consequently, there is an impetus to develop predictive models for these processes that can be readily rescaled and integrated into larger system models. Such analysis tools provide the ability to evaluate each technique on a comparable basis with respect to processing rates. This manuscript describes the current models for the carbon dioxide reduction processes under parallel developmental efforts. Comparison to experimental data is provided were available for verification purposes.

Swickrath, Michael J.↗
NASA NTRSDate not supplied

Impact of the May 2024 Gannon Storm on Low Earth Orbit Dosimetric Quantities: Comparisons of the NAIRAS Model -Real Time and Re-analysis- with ISS Data

The solar storm of May 2024, the Gannon storm, led to a display of aurora over the globe. One of the less known effects of that storm is on the radiation doses in low-Earth orbit: it first led to a Forbush decrease in dose rates and then to a Solar Energetic Particle (SEP) event that increased the total dose suffered near the international space station. The Nowcast of Aerospace Ionizing RAdiation System (NAIRAS) model predicts dosimetric and radiative flux quantities for assessing human radiation exposure levels and radiation effects on flight electronic systems from the surface of the Earth to deep space. It runs in near-real-time at the CCMC, but also has a run-on-request that allows for a more precise computation thanks to carefully processed data. NAIRAS was able to compute the effects of the Gannon storm at the ISS in real-time and provide ideas of the doses encountered by the astronauts and the experiments in and outside of the station. In this work, we show the simulations of the doses encountered during the storm and compare them with several measurements at the ISS. This work shows the capabilities of NAIRAS to address the problem of the SEP events at low Earth orbit and its real-time capabilities.

Guillaume Gronoff↗
NASA NTRS2008

Assessing Requirements Quality through Requirements Coverage

In model-based development, the development effort is centered around a formal description of the proposed software system the model. This model is derived from some high-level requirements describing the expected behavior of the software. For validation and verification purposes, this model can then be subjected to various types of analysis, for example, completeness and consistency analysis [6], model checking [3], theorem proving [1], and test-case generation [4, 7]. This development paradigm is making rapid inroads in certain industries, e.g., automotive, avionics, space applications, and medical technology. This shift towards model-based development naturally leads to changes in the verification and validation (V&V) process. The model validation problem determining that the model accurately captures the customer's high-level requirements has received little attention and the sufficiency of the validation activities has been largely determined through ad-hoc methods. Since the model serves as the central artifact, its correctness with respect to the users needs is absolutely crucial. In our investigation, we attempt to answer the following two questions with respect to validation (1) Are the requirements sufficiently defined for the system? and (2) How well does the model implement the behaviors specified by the requirements? The second question can be addressed using formal verification. Nevertheless, the size and complexity of many industrial systems make formal verification infeasible even if we have a formal model and formalized requirements. Thus, presently, there is no objective way of answering these two questions. To this end, we propose an approach based on testing that, when given a set of formal requirements, explores the relationship between requirements-based structural test-adequacy coverage and model-based structural test-adequacy coverage. The proposed technique uses requirements coverage metrics defined in [9] on formal high-level software requirements and existing model coverage metrics such as the Modified Condition and Decision Coverage (MC/DC) used when testing highly critical software in the avionics industry [8]. Our work is related to Chockler et al. [2], but we base our work on traditional testing techniques as opposed to verification techniques.

Rajan, Ajitha↗
NASA NTRSDate not supplied

A Parametric Battery Model for the Conceptual Design of Electric Aircraft

Electric aircraft conceptual designs usually have an assumed specific power and specific energy for the aircraft’s energy storage system that dictates the total capacity and the peak power available. The specific energy and power are inherently linked to the state-of-charge and discharge rate from which they were derived; therefore, they will not directly correspond to the diverse circumstances encountered in various aircraft missions and flight segments. These parameters turn the battery system into a black box, disregard potential electrical restrictions, and disallow the aircraft and battery to be optimized as a system. Peering into this box, this study highlights the importance of incorporating a parametric battery model into the conceptual design workflow by splitting high-level terms such as power into voltage and current and investigating their variability during the discharge process. Through the modeling of these more detailed parameters, this methodology shows the feasibility of using low states-of-charge for contingency operations, including the end of the reserve mission, expanding the amount of usable capacity for electric aircraft. Stark differences in aircraft capabilities can arise between varying fidelity battery models due to late-mission, high-power flight operations. This parametric battery model effectively captures these differences by evaluating the limitations that arise within the individual battery cells and the aircraft powertrain. This paper shows that the unusable charge of a battery is set by the balked landing power requirement and can realistically range from 5% to 44% based on assumptions. This sets the analog to unusable fuel capacity in aircraft with liquid fuel systems. Needing only aircraft- and mission-level inputs and only seconds of run time, this model is a prime fit for the fast, accurate exploration of the electric aircraft conceptual design space.

Battery↗
NASA NTRS2004

The Role of Integrated Modeling in the Design and Verification of the James Webb Space Telescope

The James Web Space Telescope (JWST) is a large, infrared-optimized space telescope scheduled for launch in 2011. System-level verification of critical optical performance requirements will rely on integrated modeling to a considerable degree. In turn, requirements for accuracy of the models are significant. The size of the lightweight observatory structure, coupled with the need to test at cryogenic temperatures, effectively precludes validation of the models and verification of optical performance with a single test in 1-g. Rather, a complex series of steps are planned by which the components of the end-to-end models are validated at various levels of subassembly, and the ultimate verification of optical performance is by analysis using the assembled models. This paper describes the critical optical performance requirements driving the integrated modeling activity, shows how the error budget is used to allocate and track contributions to total performance, and presents examples of integrated modeling methods and results that support the preliminary observatory design. Finally, the concepts for model validation and the role of integrated modeling in the ultimate verification of observatory are described.

Mosier, Gary E.↗
NASA NTRS2011

The Development of Models for Carbon Dioxide Reduction Technologies for Spacecraft Air Revitalization

Through the respiration process, humans consume oxygen (O2) while producing carbon dioxide (CO2) and water (H2O) as byproducts. For long term space exploration, CO2 concentration in the atmosphere must be managed to prevent hypercapnia. Moreover, CO2 can be used as a source of oxygen through chemical reduction serving to minimize the amount of oxygen required at launch. Reduction can be achieved through a number of techniques. The National Aeronautics and Space Administration (NASA) is currently exploring the Sabatier reaction, the Bosch reaction, and co-electrolysis of CO2 and H2O for this process. Proof-of-concept experiments and prototype units for all three processes have proven capable of returning useful commodities for space exploration. While all three techniques have demonstrated the capacity to reduce CO2 in the laboratory, there is interest in understanding how all three techniques would perform at a system-level within a spacecraft. Consequently, there is an impetus to develop predictive models for these processes that can be readily re-scaled and integrated into larger system models. Such analysis tools provide the ability to evaluate each technique on a comparable basis with respect to processing rates. This manuscript describes the current models for the carbon dioxide reduction processes under parallel developmental e orts. Comparison to experimental data is provided were available for veri cation purposes.

Swickrath, Michael J.↗
NASA NTRS1986

Simulation model for plant growth in controlled environment systems

The role of the mathematical model is to relate the individual processes to environmental conditions and the behavior of the whole plant. Using the controlled-environment facilities of the phytotron at North Carolina State University for experimentation at the whole-plant level and methods for handling complex models, researchers developed a plant growth model to describe the relationships between hierarchial levels of the crop production system. The fundamental processes that are considered are: (1) interception of photosynthetically active radiation by leaves, (2) absorption of photosynthetically active radiation, (3) photosynthetic transformation of absorbed radiation into chemical energy of carbon bonding in solube carbohydrates in the leaves, (4) translocation between carbohydrate pools in leaves, stems, and roots, (5) flow of energy from carbohydrate pools for respiration, (6) flow from carbohydrate pools for growth, and (7) aging of tissues. These processes are described at the level of organ structure and of elementary function processes. The driving variables of incident photosynthetically active radiation and ambient temperature as inputs pertain to characterization at the whole-plant level. The output of the model is accumulated dry matter partitioned among leaves, stems, and roots; thus, the elementary processes clearly operate under the constraints of the plant structure which is itself the output of the model.

Raper, C. D., Jr.↗